Why is it when I change my animation and delete keyframes it deletes keyframes from a different animation?
What's happening is not what you're describing, actually you're completely misguided because one of your window is completely collapsed, so when you think you're deleting the keyframes of an action you're actually deleting the keyframes of another. So first of all, uncollapse your window, and now you'll see the action that is really selected:



To delete actions, there are several ways, one is to go to the Outliner, select Blender File in the dropdown menu, unfold the action menu, select and right click Delete. You can also shift click on the X, the action has a 0 in front of its name, meaning that it doesn't have any user anymore, it won't be here when you'll reopen the file. You can't delete actions with the NLA.